Theorem 1 [1]}
Let \(Z_{1}\) , \(Z_{2}\)  be Gaussian random vectors with positive semi-definite covariance matrices \(K_{1}\)  and \(K_{2}\) , respectively. If there exists a positive semi-definite matrix \(B^{*}\)  such that
\(\left( B^{*} + K_{1} \right)^{-1} + M_{1} = \mu \left( B^{*} + K_{2} \right)^{-1} + M_{2},\) 
